Simplifying radicals is a fundamental algebra skill that involves identifying and extracting perfect square factors from under the radical symbol. The goal is to express the radical in its simplest form by factoring out perfect squares and leaving only non-perfect square factors under the radical.

Perfect Squares and Common Factors

Perfect squares are numbers that can be expressed as n² for some integer n. Recognizing common perfect squares (4, 9, 16, 25, 36, 49, 64, 81, 100) helps simplify radicals quickly. Always look for the largest perfect square factor to fully simplify in one step.

• Common perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
• Product rule: √(a×b) = √a × √b (same index required)
• Quotient rule: √(a/b) = √a / √b (for b ≠ 0)
• Power rule: (√a)ⁿ = √(aⁿ) or a^(n/2)
• Simplify by extracting all perfect square factors

Sources & References